Twitter isn't programmed to show any user the specific people looking at certain tweets. It is actually new for some other social sites to be programmed to show such information.
The only way to know who sees your tweets is to look at the amount of followers on your profile. Everything tweeted on a profile shows up on all the followers' Twitter feed. Not allowing people to see who views their tweets is a reverse privacy feature Twitter has in place. Since a person can't see who views their tweets, he should be careful about what he posts on the site. The number of followers a person has is listed on his account page, under the heading.